Bayesian Modeling Using Winbugs
by Ntzoufras, IoannisEdition: 1st
Format: Hardcover
Pub. Date: 2009-02-03
Publisher(s): Wiley
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Summary
The BUGS (Bayesian inference Using Gibbs Sampling) project is concerned with free, flexible software for the Bayesian analysis of complex statistical models using Markov Chain Monte Carlo (MCMC) methods. It details the various and commonly-used modeling techniques that are employed by statisticians in a multitude of sciences such as; biostatistics and social science; actuarial science environments. This book presents the reader with a clear and easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. Emphasis is given to Generalized Linear Models (GLMs) familiar to most readers and researchers. Detailed explanations cover model building, prior specification, writing WinBUGS code, and analyzing and interpreting WinBUGS output. Also features comprehensive problems and examples.
Author Biography
Ioannis Ntzoufras, PhD, is Assistant Professor of Statistics at Athens University of Economics and Business (Greece). Dr. Ntzoufras has published numerous journal articles in his areas of research interest, which include Bayesian statistics, statistical analysis and programming, and generalized linear models.
Table of Contents
| List of Figures | |
| List of Tables | |
| Preface | |
| Acknowledgments | |
| Acronyms | |
| Introduction to Bayesian inference | |
| Introduction: Bayesian modeling in the 21st century | |
| Definition of statistical models | |
| Bayes theorem | |
| Model based Bayesian inference | |
| Inference using conjugate prior distributions | |
| Non Conjugate Analysis | |
| Problems | |
| Markov Chain Monte Carlo Algorithms in Bayesian Inference | |
| Simulation, Monte Carlo integration and their implementation in Bayesian inference | |
| Markov chain Monte Carlo methods | |
| Popular MCMC algorithms | |
| Summary and closing remarks | |
| Problems | |
| The WinBUGS software: Introduction, Set-up and Basic Analysis | |
| Introduction and historical background | |
| The WinBUGS environment | |
| Preliminaries on using WinBUGS | |
| Building Bayesian models in WinBUGS | |
| Compiling the model and simulating values | |
| Basic Output analysis using the Sample Monitor Tool | |
| Summarizing the procedure | |
| Chapter summary and concluding comments | |
| Problems | |
| The WinBUGS Software: Illustration, Results and Further Analysis | |
| A complete example of running MCMC in WinBUGS for a simple model | |
| Further output analysis using the inference menu | |
| Multiple chains | |
| Changing the properties of a figure | |
| Other tools and menus | |
| Summary and concluding remarks | |
| Problems | |
| Introduction to Bayesian models: Normal models | |
| General modeling principles | |
| Model specification in Normal regression models | |
| Using vectors and multivariate priors in normal regression models | |
| Analysis of variance models | |
| Problems | |
| Incorporating categorical variables in normal models&further modeling issues | |
| Dummy variables and design matrices | |
| Analysis of variance models using dummy variables | |
| Analysis of covariance models | |
| A Bioassay example | |
| Further modeling issues | |
| Closing remarks | |
| Problems | |
| Introduction to generalized linear models: Binomial and Poisson data | |
| Introduction | |
| Prior distributions | |
| Posterior inference | |
| Poisson regression models | |
| Binomial Regression Models | |
| Models for contingency tables | |
| Problems | |
| Generalized linear models: Models for positive continuous data, count data and other GLM based extensions | |
| Models with non-standard distributions | |
| Models for positive continuous response variables | |
| Additional models for count data | |
| Further GLM based models and extensions | |
| Problems | |
| Bayesian Hierarchical models | |
| Introduction | |
| Some simple examples | |
| The generalized linear mixed model formulation | |
| Discussion, closing remarks and further reading | |
| Problems | |
| The predictive distribution and model checking | |
| Introduction | |
| Estimating the predictive distribution for future or missing observations using MCMC | |
| Using the predictive distribution for model checking | |
| Using cross-validation predictive densities for model checking, evaluation and comparison | |
| Illustration of a complete predictive analysis: Normal regression models | |
| Discussion | |
| Problems | |
| Bayesian Model and Variable Evaluation | |
| Prior predictive distributions as measures of model comparison: Posterior model odds and Bayes Factors | |
| Sensitivity of the posterior model probabilities: The Bartlett-Lindley paradox | |
| Computation of the marginal likelihood | |
| Computation of the marginal likelihood using WinBUGS | |
| Bayesian variable selec | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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